In fact, I do believe that perhaps the same Nash equilibrium failure that applies to scripting (as stated above) may apply in the cross-partition design for asset transfers because there is a cascade of history. I need to think about this more. I will try to remember to comment on this point later.
I've touched on this before, but you've reminded me again; partitions are the antithesis of consensus. Taking things to the extreme is helpful to illustrate the problem: with infinite partitions, in bitcoin, you are left with the DAG of the UTXO set, and no blocks or any agreement on what the order of transactions should be, in other words,
no consensus. The LCR in bitcoin constantly forces miners to chose between candidate potential partitions (orphan chains). The nash equilibrium results in rational miners always choosing the longest branch to mine on to maximise their profits.
More completely stated, the Nash equilibrium is that there is no other strategy other than the strategy of mining on the longest chain which is visible to all nodes, i.e. that there is no superior strategy other than the one that nodes are already doing and which is known to all nodes. Whereas, as I pointed out in my video, when a node (or colluding nodes) have > 33% of the hashrate, then for Satoshi' PoW design they can apply
the selfish mining attack by withholding block solutions until the rest of the network catches up, thus the Nash equilibrium is destroyed by selfish mining in that case.
Also I have pointed out in my video and the follow up posts in this thread about a
meta issue that destroys the Nash equilibrirum, that for the case where there are external failures (external to the block chain's perspective of itself) due to external actuation of cross-partition state (even if the block chain thinks it is enforcing a strict partitioning with no cross partition state), the Nash equilibrium fails because the entire coin fails, thus the validators of partitions can't trust the validators of other partitions (because although they get their block reward, the external market value of the reward fails). It remains under study whether this applies to asset transfers too (or just to partitioning of scripts) and whether it applies for asset transfers in the strict partitioning block chain (which I argued in my video is immune to the problem) and/or in the cross-partitioning block chain (which I did not address in my video and Fuserleer raised this point hence).
I hope readers don't get confused that I am making a distinction between when cross partitioned state is occurring by-design on the block chain and when it occurs externally because it can. For scripting it is impossible to enforce a strict partitioning because it is very clear that the external actuation can inject state from one partition into another partition (and even though the block chain can't determine this, the external users can and the external users can experience failure that the block chain is entirely unaware of due to this external Turing completeness, which is a very deep, meta, high IQ concept that apparently most people wouldn't think of ... note smooth indicated to me in a PM that he had thought of this issue of external Turing completeness before too). For asset transfers (no scripting), it is not yet 100% clear to me. I need to think about it more.
Talking about partition unification for a moment; if two partitions are totally separate, merging them doesn't have any consequences for ordering because the individual transactions in each partition have been separate from each other, you can order them however you like as long as you obey the parent/child relationship in each partition.
Yes as long as the state from the two partitions did not leak into each other
by any means (including the external meta case mentioned again above).